FloatingPointRepresentation

# exercise 17 what are the possible values for 11 a b

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Unformatted text preview: are the possible values for 1;1 a b where a and b are both nonnegative (positive or zero)? Exercise 18 What are sensible values for the expressions 1=1? 1=0, 0=1 and Exercise 19 Using the 1950's convention for treatment of division by zero mentioned above, the expression (1=0)=10000000) results in a number very much smaller than the largest oating point number. What is the result in IEEE arithmetic? The reader may very reasonably ask the following question: why should 1=0 have the value 1 rather than ;1? This is the main reason for the existence of the value ;0, so that the conventions a=0 = 1 and a=(;0) = ;1 may be followed, where a is a positive number. (The reverse holds if a is negative.) It is essential, however, that the logical expression h0 = ;0i have the value true while h1 = ;1i have the value false. Thus we see that it is possible that the logical expressions ha = bi and h1=a = 1=bi have di erent values, namely in the case a = 0, b = ;0 (or a = 1, b = ;1). This phenomenon is a direct...
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